Questions: Re-write the quadratic function below in Standard Form y=-(x-1)^2+4

Transcript text: Re -write the quadratic function below in Standard Form \[ y=-(x-1)^{2}+4 \]

Solution

Solution Steps

To rewrite the given quadratic function in standard form, we need to expand the squared term and simplify the expression. The standard form of a quadratic function is \( y = ax^2 + bx + c \).

Step 1: Expand the Squared Term

Given the quadratic function: \[ y = -(x - 1)^2 + 4 \] First, expand the squared term \((x - 1)^2\): \[ (x - 1)^2 = x^2 - 2x + 1 \]

Step 2: Distribute the Negative Sign

Next, distribute the negative sign through the expanded term: \[ -(x^2 - 2x + 1) = -x^2 + 2x - 1 \]

Step 3: Combine Like Terms

Add the constant term \(4\) to the expression: \[ y = -x^2 + 2x - 1 + 4 \] Combine the constant terms: \[ y = -x^2 + 2x + 3 \]

Final Answer

The quadratic function in standard form is: \[ \boxed{y = -x^2 + 2x + 3} \]

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